We may now relativize our definitions to the context of Scott spaces. We say that a lattice \(L\)  has a Scott-topological representation if \(L\)  is isomorphic to \(\Gamma (P)\)  for some poset \(P\) , and ask:
 
Which lattices have Scott-topological representations?

Although some work has been done on this problem, [1]}, as of now it remains open. In the special case of continuous domains a very pleasing answer was given independently by Jimmie Lawson, [2]}, and Rudolf-Eberhardt Hoffmann, [3]}. They showed that a lattice \(L\)  has a Scott-topological representation \(\Gamma (P)\)  for some continuous domain \(P\)  if and only if \(L\)  is completely distributive.
